This paper attempts to determine conditions under which distributed lag analysis is appropriate. Results indicate that lag functions are stable and linear under fairly general (but constant) objective criteria and decision constraints as long as the underlying economic environment is characterized by a stationary Gauss-Markov process, and observed environmental variables are Gaussian perturbations of that process. The results appear particularly useful for specifying the lag distribution inherent in subjective parameters in specific decision problem contexts. 1. INTRODUC'TION IN AN EARLIER PAPER, Taylor [11] dealt with the problem of determining lag distributions on the basis of optimization assumptions in a dynamic model of uncertainty. Taylor's conclusions, however, are somewhat disturbing in that they indicate only a narrow class of decision problems with uncertainty can be studied in a distributed lag framework. Taylor addresses only an exemplary model of inventory control and by assuming that (i) the firm's cost function can be expressed as a sum of strictly quadratic and linear terms, (ii) all production constraints are linear equalities, and (iii) observed demands are perturbations of unobserved components which follow a Gauss-Markov process, he is able to show that a distributed lag exists in the decision rule. By making yet additional assumptions, he is also able to demonstrate stability of the lag distribution. The purpose of this paper is to generalize the class of decision-makers' objective criteria and the constraint set description under which distributed lag analysis can find some theoretical justification. Although Taylor relies heavily on Kalman filtering theory to derive his results, the equivalent Bayesian approach is used explicitly in this paper for purposes of completeness and continuity.2 Results show that the lag function is stable and linear under more general conditions than Taylor's, although the lag function may enter the resulting econometric model nonlinearly. If econometric investigators are willing to consider nonlinear functions of lag distributions (or approximation of nonlinear functions by linear functions), the results should provide a basis for distributed lag analysis in a much broader class of problems than do Taylor's previous results. Furthermore, it is found that econometric equations which include the distributed lag linearly may exist outside of the set of cases considered by Taylor. The following section begins by specifying the general decision theoretic framework in which we shall operate throughout the paper. The existence of lag functions is made evident. In Section 3, Taylor's environmental system is

Analysis of the growth record of many economies indicates that foreign capital is an important factor in the process of economic development. For many developing countries, a continuing flow of foreign funds is necessary if desired growth targets are to be achieved. These funds are most likely to be in the form of loans rather than grants. This link between economicdevelopment and debt accumulation manifested itself in the enormous growth of less developed countries’ (LDCs) external indebtedness in recent years, especially after the oil crisis of 1973.

and FORTRAN IV which is designed to accommodate most researchers' everyday econometric needs. However, this program is particularly useful when spectral methods are combined (in an ex post sense) with regression and simultaneous equations estimation., Residuals from regression or simultaneous equations estimation are easily saved by EAS and used in later spectral computations by using only two program statements.1 All spectral computations are highly efficient since the fast Fourier transform techniques developed by Cooley and Tukey [2] are used throughout. The program also allows algebraic expressions to be used directly in regression statements to define dependent or independent variables. Hence, special regression equations like the harmonic analysis model can be easily estimated with a single program statement. A partial enumeration of the program's capabilities is as follows: ordinary and weighted least squares regression; multivariate regression and estimation of Zellner's seemingly unrelated regression system; structural estimation of simultaneous equations by two-stage least squares, three-stage least squares, limited information maximum likelihood, k-class, double k-class, h-class, and Nagar's minimum bias k-class methods; power spectrum analysis, cross spectrum analysis, and simple frequency domain regression; random number generation and Monte Carlo methods; principal components analysis; estimation of partially nonlinear models by likelihood search techniques; and estimation of certain distributed lag models by Dhrymes' [3] methods. The program accommodates problems in which the sample size and number of yariables do not exceed 32,767 and 1,823, respectively, but the dynamic core allocation features of PL/1 are used to economize on all smaller problems. The design of the program is especially useful when a large data bank (subject to the abQve limitations) is to be maintained, updated, and periodically accessed for various types of econometric analyses. Most small- to medium-sized

This paper examines the behavior of a competitive firm under price uncertainty where a futures market exists for the commodity produced by the firm. Working with the Sandmo approach, we found that production decisions depend only on the futures market price and input costs; the subjective distribution of future spot price affects only the firm's involvement in futures trading. Conditions are then determined under which a firm will either hedge, speculate by buying futures contracts, or speculate by selling futures contracts. The results indicate that an important social benefit derived from the existence of a futures market is to eliminate output fluctuations due to variation in producers' subjective distributions of future spot price.

I. The model 140.—II. Marginal effects of taxes and subsidies, 142.—III. The role of risk preferences, 143.—IV. Relative effectiveness of taxes and subsidies, 145.—V. Conclusions, 147.